The Dirichlet Problem for the Monge-ampère Equation in Convex (but Not Strictly Convex) Domains
نویسندگان
چکیده
It is well-known that the Dirichlet problem for the MongeAmpère equation det Du = μ in a bounded strictly convex domain Ω in R has a weak solution (in the sense of Aleksandrov) for any finite Borel measure μ on Ω and for any continuous boundary data. We consider the Dirichlet problem when Ω is only assumed to be convex, and give a necessary and sufficient condition on the boundary data for solvability.
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